| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Difficulty | Standard +0.3 This is a straightforward application of standard regression formulas: finding r from the product of regression slopes, performing a routine correlation test, using the property that regression lines intersect at means, and making a prediction with basic reliability comment. All steps are direct recall of textbook methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09c Calculate regression line5.09e Use regression: for estimation in context |
9 For a random sample of 10 observations of pairs of values $( x , y )$, the equations of the regression lines of $y$ on $x$ and of $x$ on $y$ are
$$y = 4.21 x - 0.862 \quad \text { and } \quad x = 0.043 y + 6.36 ,$$
respectively.\\
(i) Find the value of the product moment correlation coefficient for the sample.\\
(ii) Test, at the $10 \%$ significance level, whether there is evidence of non-zero correlation between the variables.\\
(iii) Find the mean values of $x$ and $y$ for this sample.\\
(iv) Estimate the value of $x$ when $y = 2.3$ and comment on the reliability of your answer.
\hfill \mbox{\textit{CAIE FP2 2013 Q9}}